Tivat has a numerous shops selling Women's and Men's Clothes. Most of them sell the items imported from Italy. You might find something nice at the good price. The photos show some things from Ultima Moda shop on the promenade.
Niksen Trade is famous for production of healthy ecological meat and other meat product. Their own store in Tivat is great place to try some Montenegrian specialities. If the Custom of your country allowes, you can take some of that home.